Abstract: This paper is an articulation and defense of a trope-bundle theory
of material objects. After some background remarks about objects and tropes,
I start the main defense in Section III by answering a charge frequently made
against the bundle theory, namely that it commits a conceptual error by saying
that properties are parts of objects. I argue that there's a general and intuitive
sense of "part" in which properties are in fact parts of objects.
This leads to the question of qualitative unity: in virtue of what are certain
properties unified as parts of an object? In Section IV I defend an account
of unity for complex material objects. It turns on the thesis that the properties
of such objects are structural properties. After addressing some objections,
I turn in Section V to the question of unity for simple material objects. Here
a different and more radical account is needed for simples, since they do not
have structural properties, are not subsumed by the account of Section IV.
I defend the view that a simple object just is a simple property, so that identity
delivers the desired unity.

I. Introduction

It's hard
to deny that there are natures or ways of being. They are
most evident in our own conscious experiences, but the "what it's like" of
consciousness is really just a special case of a way of being: it is a way
an experience is. But the non-conscious parts of our world are various ways
too. And how could it be otherwise? How could there be being without a way
of being? To be is to be some way or other. I'll call these ways properties.

If there are properties,
must there be, in addition to them, non-property bearers of those
properties? A traditional line of thinking insists that yes, properties require
something else, something that is not itself a property, but nevertheless must
exist if properties do. Call this thing a substratum.[1] Here is Locke, expressing
this tradition in a well-known passage from the Essay (II.xxiii.1):

The Mind being,
as I have declared, furnished with a great number of the simple Ideas, conveyed
in by the Senses, as they are found in exteriour things, or by Reflection on
its own Operations, takes notice also, that a certain number of these simple
Ideas go constantly together; which being presumed to belong to one thing,
and Words being suited to common apprehensions, and made use of for quick dispatch,
are called so united in one subject, by one name; which by inadvertency we
are apt afterward to talk of and consider as one simple Idea, which indeed
is a complication of many Ideas together; Because, as I have said, not imagining
how these simple Ideas can subsist by themselves, we accustom our selves, to
suppose some Substratum, wherein they do subsist, and from which they do result,
which therefore we call Substance.

Here and elsewhere, Locke gives substrata
two roles to fill: First, properties (what Locke here calls "ideas") do not
float in isolation from one another. Rather, they are clustered into what we
think of as objects. So a unifier of properties is required, something
to hold properties together in these clusters. Second, properties cannot exist
on their own: there must be something in which they "subsist". So a supporter of
properties is required, something that keeps them in existence. The roles of
unifier and supporter are distinct,[2] but Locke says we postulate a single
thing to fill both: substratum.

As an account of where our idea of substratum comes from,
Locke's line of reasoning may be right. But as an argument for the existence
of substrata, it is unconvincing. Even if properties must be unified, why can't
their unity be found in their relations to one another? And even if the properties
we observe--those that Locke appeals to--are dependent entities requiring support,
why should this be true of all properties? And when support is needed,
why must such support be found outside the category of property? Why, that
is, can't dependent properties be supported by other properties? Enter the
bundle theory: the world does not contain substrata in addition to properties.
To be sure, there are what we may neutrally call substances or objects--chairs,
trees, human beings, electrons, stars--but these objects are not, nor do they
contain as constituents, substrata: they are merely bundles of properties.
Not only must a being be some way or other, it is exhausted by ways
of being.

Such
is the bundle theory in its starkest form, and its attractions are well known.
It removes the need for substrata, which some philosophers have found to be
problematic if not incoherent. And it is typically part of an elegant one-category
ontology, one that includes only ways of being as basic constituents. However,
I will not spend much time in this paper praising the virtues of the bundle
theory, at least not in the sense of giving positive arguments for it over
its rivals. Rather, this paper will be primarily defensive. My aim is to articulate
the central features of the bundle theory and defend it against some common
objections. As one can infer from Locke's remarks, two of the most pressing
problems for any bundle theory are in accounting for the
(alleged) dependence of and unity among properties. I've already indicated
in brief how I would respond to these challenges, but more is needed than the
rhetorical questions above.

The paper is structured as follows: After some
preliminaries in Section II, I'll start the defense in Section III by answering
a charge frequently made against the bundle theory, namely that it commits
an egregious conceptual error in saying that properties are parts of
objects. I'll argue that there's a general and intuitive sense of 'part' in
which properties are in fact parts of objects. This will lead to the question
of unity raised above: in virtue of what are certain properties unified as parts
of an object? In Section IV, I'll defend a "principle of unity" for ordinary,
complex objects. The principle will explain, as a corollary, the sense in which
the properties of ordinary objects are dependent entities, though in a way
that does not require that they depend on a substratum. After defending this
principle from some objections, I will turn in Section V to the question of
unity for simple objects; here a different and more radical account
will be needed, for these sorts of objects are not subsumed by the principle
in Section IV.

II. Objects and Properties

To bring into focus my favored version of the bundle
theory, I'll start with some preliminary points about objects and properties.

1.Objects

The bundle theory offers an account of the ontological structure of
objects. But it does not offer an analysis of the concept object.
We have a rough understanding of what an object is: it is a unified, persisting,
independent being. But I doubt one can turn these criteria into informative,
conceptually necessary and sufficient conditions for something's being a object.[3]
And in any case, whether or not such an analysis is possible, it is not the
aim of the bundle theory to provide it. Whether something counts as an object
may for the purposes of this paper be taken as a primitive fact about it. An
account of its ontological structure, on the other hand, goes deeper.

The bundle theory's
claim that an object is some bundled properties may be refined in
a number of ways, including the following: Identity: an object is
numerically identical with some bundled properties. Here identity is a one-many
relation. Supervenience:
an object supervenes on some bundled properties, where this is understood to
be some relation that, while entailing a strong dependence of object on properties,
is weaker than identity. Elimination: strictly speaking, there are
no objects--suppose the (loose) requirements listed earlier are never appropriately
satisfied--but the closest things in the world answering to our concept of
object are property bundles. In spite of their differences, these
refinements are all instances of the bundle theory, for on all of them bundled
properties exhaust the being of objects. It is the bundle theory in
this general sense, not any of these refinements, that I will defend in this
paper.[4]

Finally, I will in
this paper restrict the bundle theory to material objects; I'll have nothing
to say about immaterial objects such as souls or abstract objects such as numbers.

2. Properties

I've already identified properties as ways of being. This much,
I believe, should be uncontroversial. But I will assume a further and more
controversial thesis about properties, namely that they are tropes,
particularized ways incapable of being instantiated by (wholly) distinct objects
at the same time. Tropes are not, and cannot be, a "one across many".[5]
So the yellowness of a tennis ball is not the same as the yellowness of another
tennis ball, even though these two properties resemble each other, perhaps
exactly. On the bundle theory defended here, then, an object is some bundled
tropes.

I should
also note in connection with this that I'll follow Campbell (1990) and others
in taking tropes to be simple in the following sense: tropes do not
have as constituents, and are not reducible to, items in other ontological
categories. So, for example, a trope is not an object's having a universal.
Such an account of tropes would immediately lead the bundle theorist into trouble:
Imagine saying that an object is some bundled tropes, each of which
is an object's having a universal. If the latter object is the former,
then the account is circular; if not, a vicious regress threatens. However,
while tropes are simple in the above sense, this does not mean that they must
lack parts altogether, for a trope can have other tropes as parts. The yellowness
of a tennis ball has as parts the yellowness of the ball's left half and the
yellowness of its right half. Far from making trouble for the bundle theory, this sort
of complexity, as I hope to show, points the way toward an account of property-unity.

III.
Qualitative Parts

1. Can Properties Be Parts?

If the bundle theory is true,
then properties are parts of objects. Some philosophers will object that this
commits a category mistake. Hoffman and Rosenkrantz, for example, criticize
"collectionism" (their name for the bundle theory) because it fails to respect

the
intuitive datum that no feature of a substance is a part of that
substance. For example, intuitively, the right and left halves of a material
object, o,
are parts of o, but the shape and the size of o are not parts
of o.... [Collectionism's]
implication that the shape of o is a part of o also conflicts
with another datum for a theory of substance: that the parts of a material
substance are either material substances or portions of matter. That collectionism
has implications which conflict with these data is an indication of a category
mistake in the identification of substances with collections.[6]

Earlier I noted that a bundle
theorist needn't identify an object with a bundle of properties,
but Hoffman and Rosenkrantz's remarks about parthood also threaten supervenience
and (perhaps) eliminativist versions of the bundle theory.

Hoffman and Rosenkrantz
say it is an "intuitive datum" that properties are not parts of objects.
Below I will propose an intuitive sense of 'part' according to which they are.
But for now it's worth exploring why it does seem on the face of it that properties
cannot be parts of objects. I suggest this appears to be so because of the
following:

(1) Parts are independent, both of each other and of the whole
of which they are parts. But properties are dependent, both on each other
and on the objects of which they are properties. A chair's leg can exist
separately from the chair and from other parts of the chair. But one cannot
separate (without destroying it) the color of a table from the table or from
other properties (e.g., the extension) of the table.

(2) An object typically comes into being
by the arrangement of pre-existing (soon-to-be) parts. A house, for example,
comes into being
by taking bricks, planks, shingles, etc. and arranging them according to
a blueprint. But an object never comes into existence by bringing together
pre-existing properties (a size, a shape, and so on) and arranging them,
for such properties do not exist before the object comes into being.

(3) Parts are additive: they
permit the arbitrary addition of further parts. For example, there is no barrier
to adding a fifth leg to a table, or gluing more fuzz on a tennis ball. In
general, if some parts compose a whole in virtue of standing in some relation
R to one another, then it should be at least logically possible to bring something
new into R with these parts so that a larger whole is composed. But properties
are not additive in this sense: It is generally speaking not possible to add
a new property to an object without destroying some others. Our yellow tennis
ball cannot take on redness or squareness, at least not while retaining its
current color and shape.

I do not wholly endorse these claims; the extent to
which I do will become clear in the last Section. But I do think (1)-(3) push
us toward an important thesis about properties. But this thesis is not that
properties cannot be parts. Rather, (1)-(3) seem to show that properties typically
are not the sort of parts that are independent, arranged, and additive. These
three features hold, not of parts generally, but only of substantial parts,
parts that are themselves objects. The proper conclusion to draw from (1)-(3)
is that properties typically are not substantial parts of objects.

However,
this reply will seem ad hoc absent some independent reasons for thinking
that properties can be parts. What the bundle theory calls for is some independently
plausible, general conception of parthood according to which an object can
have properties as parts. On the most general conception of parthood, I submit,
the parts of something exhaust its being in the sense that it is nothing
more than, nothing over and above, its parts related in some way or other.[7]
More formally:

(P) B is a part of A iff there are Cs such that (i) A is the Cs related
in certain ways, and (ii) B is one of the Cs.

Those who object to the grammatically
questionable 'A is the Cs'[8] can
substitute for it 'A is nothing over and above the Cs' or 'the Cs exhaust the
being of A', where the original 'is' or these two substitutes may be taken
in any of the senses listed earlier: identity, supervenience, or elimination.
(Elimination is still an option here, for B may
be a part of A only in the sense that B is a part of the
closest thing answering to our concept of A.)

(P) is intended to be
flexible in a number of respects. For one thing, 'related in certain ways'
can be read as one likes, depending on one's preferred restrictions on composition.
I'll return to this issue shortly. For immediate purposes, however, the most
important respect in which (P) is flexible is that does not put restrictions
on what can count as a part. It is compatible with (P) that a table, for example,
has objects as parts: a table is some pieces of wood related in certain ways,
and is some molecules..., and is some atoms..., etc. These objects are substantial
parts of the table at different mereological levels. Yet (P) also allows something
to have parts belonging to different ontological categories. For example, (P)
allows for temporal parts: a performance is various shorter events related,
say, spatiotemporally and causally. If an object has temporal parts, then the
object is some time-slices related in certain ways as well. And most importantly
for the bundle theorist, (P) allows for properties to be parts. If the bundle
theory is true, the table is some properties related in certain ways. Note,
too, that even if the table includes a substratum, the table still has properties
as parts: the table is the substratum and some properties related in certain
ways.[9]

Now there is to be sure a reductionist or "bottom-up" character to (P)
that some will find objectionable, especially if the 'is' in clause (i) is
read as identity. Anything that is just its parts (of any sort) related in
certain ways, the objection goes, lacks the sort of autonomy and unity required
of entities in their own right, i.e., of substances. This is not the place
to confront this larger issue in any detail; I will mention just two points
in reply: First, there is nothing in (P) requiring that the concept of
an object's parts in a given case be conceptually prior to the concept of that
object. The ontological priority of parts over wholes that (P) entails need
not be reflected by any conceptual priority of part-concepts over whole-concepts.
So, for example, even if an animal is just some organs arranged in a certain
way, this is compatible with our being unable to conceptualize these as organs
independently of conceptualizing them as parts of a larger animal. Second,
and more importantly, the main point of (P) is just to articulate an intuitive
notion of parthood according to which properties can be parts. If it turns
out that (P) requires modification to handle "top-down" cases in which wholes
have an ontological priority over their parts, I see no reason to think that
the modified version would prohibit properties from being parts.

It will be
useful before moving on to introduce some terms for the two kinds of part most
relevant to this paper. Parts that are themselves objects I have already
called, following a common usage, substantial parts. If an object
has substantial parts, I will say it is substantially complex. Parts
that are properties go under various names. Williams (1953) speaks of properties
as "fine parts or abstract components" of objects; Paul (2002) calls them "logical
parts". I will call them, somewhat tendentiously, qualitative parts. If an
object has qualitative parts, I will say it is qualitatively
complex.

2. Principles of
Unity

On the bundle theory, an object is some properties related in certain
ways: these are its qualitative parts. Parts of any kind, however, require
a principle of unity.[10]
A principle of unity is a relation among an object's parts, a relation in virtue
of which they are parts of the object.
As I noted earlier, I'm taking object here to be primitive, so a principle
of unity will not deliver an analysis of objecthood. It will instead deliver
something less ambitious: an account of that in virtue of which some Cs
(objects or properties) are a given object's (substantial or qualitative) parts.

When I later propose
a principle of qualitative unity, then, I will not attempt to account for the
conditions under which some properties bundle into an object. The approach,
that is, will not be of the form, 'Take some properties. Under what conditions
are they qualitative parts of an object?'[11]
Rather, it will be of the form, 'Take an object. What relation unifies certain
properties so that the object has these properties as qualitative parts?' In
a certain respect, then, the order of inquiry here will not mirror what is,
so to speak, the metaphysical order. Metaphysically, properties are 'first';
that is, they are the primary beings; the unifying relation among them is second,
and objects are third. But the order of inquiry in what follows starts with
objects, taking them for granted.

Although
my concern here is with the principle of qualitative unity, it will be useful
to start with the principle of substantial unity. Recent metaphysics has revealed
several candidate principles of substantial unity. Take a substantially complex
object. How are its substantial parts--call them the Cs--related such that
they are its substantial parts? Here are some possible answers[12]
(in some cases, the ancestral of the given relation may be more appropriate):

The Cs co-exist.

The Cs are in contact.

The Cs are bonded.

The Cs constitute
a life.

The Cs are metaphysically dependent on one another.

These options are
not exhaustive. For example, one might also wish to include substantial unity
as a primitive relation.

What are the candidate principles of qualitative unity?
In virtue of what are certain properties qualitative parts of a given object?
We find here, if not the same range of options, at least a similar range. For
example, while 'the Cs are in contact' may not comfortably apply to properties,
'the Cs spatially coincide' or 'the Cs overlap' would. And for 'the Cs are
bonded', one may wish to substitute 'the Cs are nomologically dependent on
one another'. But the list one would initially draw up would look quite similar
to the earlier list. It would even include an option for primitive unity.

Now
the first point I want to make about these candidate principles of unity--one
set for substantial parts, another for qualitative parts--is that we should
expect there to be some systematic relation between them such that our choice
of one constrains our choice of the other. First, (P) entails that substantial
parts are intimately connected in some important way to qualitative
parts. After all, if an object is its substantial parts appropriately
related and its qualitative parts appropriately related, it would
be odd in the extreme if these parts could "float free" from one another. And
while I can't see that this shows that their respective principles of unity
are systematically connected, it makes it reasonable to think they are. Second,
certain choices of principles appear to be in tension with one another. Suppose
one were to pair a modally weak principle of substantial unity--e.g., spatial
contact--with a modally strong principle of qualitative unity--e.g., metaphysical
dependence. The source of the latter's modal strength would seem to be a mystery:
why would there be such a strong principle unifying an object's properties
when its substantial parts are unified by mere contact?

In any case, my concern here in defending
the bundle theory is only with the principle of qualitative unity. I bring
up its relation to the principle of substantial unity only to make this point:
a plausible principle of qualitative unity should account for its systematic
relation to the principle of substantial unity. Any account of qualitative
unity that leaves this relation unexplained to that extent falls short.

3.
Desiderata for any Principle of Qualitative Unity

I will call this desired
feature

Coordination: A principle of qualitative unity should explain how qualitative
and substantial unity are systematically related to one another.

Coordination does not require that a principle of qualitative unity
deliver a principle of substantial unity. Indeed, in proposing the former I
will remain neutral on the latter. The idea, to look ahead a bit, will be to
take the principle of substantial unity for granted and then honor Coordination by
defining the principle of qualitative unity in terms of it.

To Coordination I add two more desiderata. Earlier I listed three reasons some may think that
properties cannot be parts. I concluded that (1)-(3) at most establish that
properties are typically not substantial parts. Now as I indicated there, I
do not wholly endorse (1)-(3): they will need to be qualified later. But any
account of the bundle theory should explain why (1)-(3) (or suitably qualified
substitutions) are true. Because (1)-(3) differentiate qualitative and substantial
parts, I call this principle

Differentiation: A principle of qualitative unity
should explain why (and when) qualitative parts are not independent, assembled,
and additive.

Finally, any philosophical account must, if pressed, eventually
postulate brute properties or relations. But this is to be avoided for as long
as possible. And furthermore, when a brute property or relation is required,
strive to make it a familiar one, not a special one postulated ad
hoc merely
to do some metaphysical job. I'll call this final desideratum

Some bundle theorists say that the unity among properties is primitive.[13]
Others spell it out as a brute modal relation.[14] I do not, of course,
think that No Mysteries is a principle so powerful that it can be
used to dismiss these bundle theorists, whose accounts of unity deserve close
study. Rather, I see No Mysteries as a methodological constraint as
well as a potential tie-breaker: an account that avoids mystery is for that
reason preferable to rivals, ceteris
paribus.[15]

IV. Qualitative Unity for Substantial Complexes

I begin with the principle
of qualitative unity for ordinary, substantially complex objects, such as chairs,
human bodies, and planets. Campbell, himself a bundle theorist, counsels against
starting with such objects.[16]
Doing so, he says, invites one to confuse (using my terms) the principle of
qualitative unity with that of substantial unity. To avoid this, Campbell advises
the bundle theorist to start with a (substantially) simple object, such as
a corpuscle in classical atomism. In reply, I agree with Campbell that the
two sorts of principle are distinct and should not be conflated. But Coordination counsels
us to investigate them jointly. Starting with substantially complex objects
allows us to do this. I'll use a tennis ball--call it 'Alpha'--as my main
example.

1. Structural Properties

If we consider
a substantially complex object such as Alpha, a principle of unity presents
itself, for all of the properties of such an object appear to be structural properties.
Armstrong introduces the notion of a structural property as a kind of complex
property, one composed of the properties of and, in most cases, relations among
that object's parts.[17] Consider
the property of being three feet long. If an object (a stick, say) has this
property, it has three substantial parts, each of which is one foot long. There's
nothing more to the object's being three feet long than the lengths of, and
relations among, these three parts. A more complex structural property is a
particular molecule's being methane.[18]
For a molecule to have this property is just for it to have five substantial
parts--a carbon atom and four hydrogen atoms--bonded to one another.

Many of
Alpha's properties are clearly structural in this sense; indeed, perhaps all of
them are structural.[19] Alpha's
color, for example, is composed of the colors of its left and right halves,
plus some relations between the halves (relations that must include, at a minimum,
the principle of substantial unity). As I'll say for short, Alpha's color is structured
on its left and right halves. In
general, a property F is structured on some objects just in case F is
a structural property composed of the properties of and relations among those
objects. Note that Alpha's color is also structured on (some of) the smaller
particles composing Alpha. In general, there's nothing wrong with one and the
same property being structured on objects at different mereological levels.

Because structural
properties are composed of properties of and relations among objects at a lower
mereological level, structural properties are dependent properties. And this
suggests that unity among structural properties is dependent as well on these
lower-level objects. Taking a cue from this suggestion, and with Coordination in mind, I propose the following principle of qualitative unity for substantially
complex objects (at a time; I will not address diachronic unity here):

(CU)
For any substantially complex object O and properties F and G, F and G are
qualitative parts of O iff F and G are both structured on the (exhaustive)
substantial parts of O at some mereological level.

(To say that substantial
parts at a mereological level are "exhaustive" means that they are all of O's
parts at that level.[20] In the
language of (P), O just is those parts related
in certain ways.)

(CU) gives the right results for Alpha's yellowness, roundness,
fuzziness, mass, and so on, for all of these properties are structured on the
left and right halves of the ball (in addition to other substantial parts of
the ball at lower mereological levels). (CU) does not, by the way, require
that unified properties be structured on the same objects at every mereological
level. Consider a wooden cube painted green. The cube's greenness and its being
made of wood are both qualitative parts of the cube. Yet these properties are
not structured on the same objects at a low mereological level, for there are
particles in the interior of the cube involved in the cube's being made of
wood that aren't involved in the cube's color, which is restricted to the surface.
Nevertheless, these properties are structured on the same objects at higher
mereological levels--for example, they are both structured on the left and
right halves of the cube--so (CU) correctly counts them as unified.

2. The
Three Desiderata

A virtue of (CU) is that it meets the three desiderata listed
earlier. (CU) most clearly satisfies Coordination, for it explicitly defines
qualitative unity in terms of substantial unity.

What about Differentiation?
Earlier I said that qualitative parts seem not to be independent, arranged,
or additive. These are some of the ways they differ from substantial parts.
(CU) delivers an explanation of why this is so.

First, qualitative parts of
substantially complex objects never occur in isolation from objects precisely
because they are structural properties, and as such cannot exist independently
of the substantial parts of an object. And given the presence of such
substantial parts, it's also clear why more than one property--more than one
qualitative part--must be present as well. Any property structured on some
substantial parts will necessarily occur with other structural properties.

Second, qualitative
parts aren't assembled because their presence depends on the (logically) prior assembly
of substantial parts. One cannot bring a tennis ball into being by first taking
a color, shape, and so on and arranging them in the right way, for these properties
are themselves composed of, and so dependent on, the properties of and relations
among certain objects, namely the substantial parts of the ball.

Third, while (CU) does not deliver a full explanation of why qualitative
parts fail to be additive, it does point in the direction of one. Consider
how such an explanation would look for Alpha's color: why can't Alpha take
on a new color, say red, while keeping its current color of yellow? The first
answer (CU) might deliver is this: Alpha's color is composed, in part, of the
colors of Alpha's left and right halves. Since these halves can't become red
without losing their yellowness, Alpha can't either. But this isn't too helpful,
since it just invites our original question again, now applied to Alpha's halves.
If (CU) is to explain in a satisfying way why Alpha cannot take on red while
retaining its current color, one must look at a low mereological level, one
in which the properties of the relevant substantial parts are not colored.
And here is where (CU) points to an explanation: I submit that if we knew what
sorts of properties were involved with Alpha's color at a low mereological
level, we would just see that Alpha's substantial parts cannot retain
these micro-properties while also taking on those required for being red.[21]
The point is perhaps clearest if the example is switched to Alpha's shape:
given how the substantial parts of Alpha must be related to one another for
Alpha to be round, we can see how they could not, while keeping these relations
to one another, also take on the relations required for the structural property
of squareness.

Finally, what about No Mysteries? To be sure, the concept of object is taken as primitive here, but this does not violate No
Mysteries, for the
concept is introduced merely to pick out our subject-matter, not as an explanatory
factor; and in any case, the notion of an object is certainly not unfamiliar.
The notion of a substantial part appealed to may seem to violate No
Mysteries.
I do not, however, take substantial parthood and with it the principle of substantial
unity to be primitive; rather, (CU) is neutral with respect to the nature of
substantial parthood. (CU) invites us to fill in this nature, not to stop here
and rest content with mystery.

3. Has There Been Progress?

In spite of meeting
the desiderata, the principle proposed here may be accused of not making progress.
Perhaps the most glaring problem of this sort for (CU) is that in appealing
to the substantial parts of a complex object, the principle appeals to entities
that must themselves be bundled properties. So they themselves must be subject
to some principle of qualitative unity. This is an important worry, and I try
to answer it in the final section. But for the moment I set it one side: the
substantial parts appealed to in (CU) may for the time being be thought of
as ontological "black boxes," objects that play an explanatory role but whose
internal structure is left unspecified.

Another apparent lack of progress,
however, can be confronted now. This problem finds inspiration in Bradley's
argument against relations, here applied to any proposed principle of qualitative
unity.[22] Any properties F and G unified
into an object, the objection goes, must be unified by some relation R1.
But R1 cannot
do its unifying work unless it itself is "bound" to F and G.
What's required, then, is some further relation, R2, to bind F, G,
and R1. The result is a vicious
regress.

The natural reply
here is to insist that R1 is an internal relation between F and G,
and so is "no addition of being" over them.[23]
In that case, the question of what unifies F, G, and R1 does
not arise--or at least, it's not distinct from the original question of what
unifies F and G, the answer to which is:
F and G themselves. This in fact is my position, though I
consider it a virtue of (CU) that it tells us, in the spirit of No Mysteries,
what this internal relation is: it is the relation of being structured on the
same substantial parts. This relation will count as internal if it is fixed
by the natures of
F and G. Assuming as I do that F and G are
essentially structured on the objects they are actually structured on, then
if F and G exist at all, they must be
unified. The relation of unification in this way ends up being nothing over
and above the related properties themselves.

There is nevertheless a third lingering worry about
progress. While the unification relation among properties may be internal,
and for that reason not lead to a regress, it nevertheless does have as a component
another relation that may seem just as problematic as the one we started with,
namely, the principle of substantial unity, on which (CU) explicitly relies.
The problem of identifying the principle of qualitative unity, the objection
goes, has been reduced one just as difficult, that of finding the principle
of substantial unity.

However, I think progress has been made by moving from
the principle of qualitative unity to the principle of substantial unity, for
three reasons: First, the very fact that (CU) systematically relates the two
principles of unity is reason to think that it may be useful in pointing the
way to a principle of substantial unity. Second, the principle of substantial
unity is a different sort of relation than the principle of qualitative unity,
one that holds among objects, not properties. Granted, since substantial parts
will themselves be bundled properties, the principle of substantial unity will
in that sense be a relation among properties. But we're no longer looking for
a relation among Alpha's properties. That is, we're now no longer
looking for a relation between, say, Alpha's yellowness and its roundness,
but rather a relation among objects at a lower, more fundamental mereological
level on which these properties are structured. Moving toward a new relation
at a more fundamental level is progress. Third, and most importantly,
by shifting the problem to that of finding the principle of substantial unity,
we've moved to an issue that's not particular to the bundle theory.
Everyone who believes in complex material objects such as Alpha will presumably
have to worry about the unifying relation among Alpha's substantial parts.
Thus the bundle theorist has made at least dialectical progress by
reducing the problem of qualitative unity to a problem that everyone but the
compositional nihilist has.

4. Non-Structural
Properties?

Another line of objection to (CU) says that not all of the properties
of a substantially complex object, not all of its qualitative parts, are structural.
Since (CU) explicitly applies only to structural properties, it will not subsume
these non-structural properties. I'll consider two such (alleged) non-structural
properties here: higher-level properties and modal properties.

Some philosophers
would say that while a complex object has structural properties, it also has
"higher-level" properties that at best merely supervene on its structural properties.
Consider color again, structured on the particles composing an object's surface.
Since this color-structural property is composed of the many properties of
and relations among these particles, it's plausible to think it could not survive
the destruction or change of even one of these particles. Yet, the argument
goes, the object's color surely could survive this: if Alpha's surface were
to lose a particle, Alpha would still have the same color, that very same trope.
The conclusion is that Alpha's color must not be a structural property after
all: it only supervenes on some structural property of Alpha. But if Alpha's
color is not a structural property, it is not subsumed by (CU), and we are
left without an account of how the color is unified with Alpha's other properties.

This
reasoning mistakes resemblance among properties for numerical identity. As
Alpha's surface gains and loses particles, it has a succession of numerically
distinct but
closely resembling color-properties, each of which is structured on, at a low
mereological level, the particles composing Alpha's surface at that time. It
is only speaking loosely that we say that Alpha has literally the same color-property
throughout these changes. Every color is a structural property--it's just that
many of these structural properties resemble each other closely enough for
us to call them "the same". But sameness here should be thought of as no more
than resemblance. This is a traditional position for a trope-theorist to take
regarding talk of "same property" among distinct objects; here the point is
just applied to one object at different times (or in different worlds).

There
is, by the way, a fallback position for the bundle theorist to move to regarding
higher-level properties. If it could be shown that Alpha's color and other
such properties merely supervene on structural properties, the bundle theorist
could exploit this dependence relation, in an ad hoc manner, to account
for the unity of Alpha's higher-level properties with each other and with Alpha's
structural properties. Call the structural properties on which Alpha's higher-level
properties supervene the latter's 'grounding properties'. The fallback principle
of qualitative unity then reads as follows:

(CU*) For any substantially complex
object O and properties F and G, F and G are qualitative
parts of O iff F and
G or their respective grounding properties are structured on the (exhaustive)
substantial parts of O at some mereological level.

So long as the grounding
relation is such that it's impossible for the properties of one object to ground
the properties of another, (CU*) will suffice to accommodate higher-level properties.[24]
In any case, postulating the brute modal relation of grounded is here
in tension with No Mysteries, so in this respect it is better to stay
with the earlier response, which keeps (CU).

Another sort of dependent property, however, is
not so easily handled. Alpha seems to have certain modal properties,
such as being essentially extended and accidentally yellow. Since such properties
are, plausibly, grounded in Alpha's non-modal, structural properties, one may
be tempted to move to (CU*) right away. But even if one moves to this fallback
principle, a problem arises in the special case of coinciding objects. Here
it's useful to switch examples to the case of the statue and the lump clay
that composes it. The statue, it is said, could not survive being squashed,
but the lump could. And this is because the statue is essentially statue-shaped,
while the lump is so only accidentally. This is a reason for thinking that
the statue and the lump are numerically distinct. If this is right, then the
properties of being essentially statue-shaped and being accidentally statue-shaped
are not unified--they are not qualitative parts of the same object--yet their
non-modal grounding properties are unified. So, the objection goes, even the
fallback (CU*) gives the wrong results in such cases

Any attempt at answering
this objection will inherit all of the difficulties of the problem of material
constitution, a problem for which there is no obvious solution.[25]
Here I'll settle for sketching one line of response, one that denies modal "properties"
are genuine properties at all. As I mentioned in the introduction, I do not
think that every predication corresponds to a way of being. And notably, modal
properties[26] such a being essentially
extended fail all of the usual tests for being a way of being, a genuine property.

(T1) Modal properties do not bestow causal powers.
A bowling ball that rolls over my foot causes pain in virtue of being massive,
but what work does its being essentially massive do? Any powers one might
think are bestowed by a modal property are already bestowed by more familiar,
non-modal properties.[27]

(T2) Modal properties are not needed as the truthmakers for modal
predications. As I mentioned earlier, the modal properties of an object are
grounded in its non-modal properties. The
non-modal properties of Alpha, for example, suffice for the truth of "Alpha
is accidentally yellow." Once God has created Alpha with all of its non-modal
properties, He need not create an additional property, being accidentally
yellow, to make this statement true. The modal predication already holds
in virtue of the relevant non-modal properties of the object.

(T3) Modal properties are
not respects in which objects can resemble one another. Fix on the distinction--one
than any realist about properties should grant--between genuine resemblance
and mere "Cambridge" resemblance, i.e., merely falling under the same predicate.
If Alpha and Beta (tennis balls) are both spherical, this seems to be a sense
in which they genuinely resemble, but if they are both essentially spherical,
is this also a case of genuine resemblance? This does not seem to be a further respect
in which they resemble one another. (Here is another way to make the same
point: Is essentially spherical a natural kind? Is it,
for example, a kind which one would ever expect to find in scientific theories?
The answers to these questions seems to be clearly No.)[28]

(T4) We are not acquainted with
modal properties in conscious experience. Sometimes negative outcomes to tests
(T1)-(T3) can be trumped by what is presented to us in experience. But experience
does not reveal modal properties to us: they are, if anything, highly theoretical
properties.

Each of these test deserves further discussion, but collectively,
they make a strong prima facie case for denying that modal properties
are ways of being. And if there are no modal properties in this sense, then
no question arises as to how they are unified with the other properties of
an object such as Alpha. As for the statue and the lump of clay that composes
it, what emerges is a familiar, if minority, position: There is just one object
there, one bundle of properties, but different ways of describing or conceiving
of it. To think
otherwise--to think that there are two objects with their own distinctive modal
properties--is to fall into the fallacy of projecting the structure of thought
and language onto the world.[29]

V. Unity for Simples

1. Expunging Objects?

It's
now time to confront a problem I mentioned earlier but did not answer. (CU)
explains qualitative unity by appealing to the notion of a substantial part.
But if the bundle theory aspires to completeness, it must also say that these
objects at lower mereological levels are themselves bundles of properties,
and one now wants to know the principle of unity for them.

The easiest move
to make here is to apply the same principle of unity to these substantial parts.
Alpha's properties are unified by being structured on, say, the left and right
halves of Alpha. Each of these halves is some bundled properties, and the properties
of each half are unified in virtue of being structured on the substantial parts
of that half, and so on. Might this continued ad infinitum? Armstrong
discusses this possibility and thinks it creates a problem for the bundle theorist:

It
is clear that many properties of particulars involve essential reference to
proper parts of these particulars. If a thing is to be a chess-board, for instance,
it must have spatial parts of a certain nature related in a certain way. These
parts, however, are particulars. It appears, then, that many of the properties
which figure in the bundle involve the notion of further particulars. Yet the
notion of a particular is the one to be analysed.

Presumably the Bundle theorist
will reply that these further particulars are themselves bundles of properties.
But these new bundles may themselves include properties which involve reference
to still further parts, which are again particulars. Now it is at least logically
possible that this process should go on ad infinitum. A particular may
lack any ultimate parts. But for such particulars, it is suggested, it is
impossible to carry out the resolution of particulars into bundles of properties.[30]

Armstrong
is not talking directly about qualitative unity here, but it's clear how the
objection would apply to the present account. If objects are complex "all the
way down"--if every object has substantial parts--then a principle of unity
appealing to structural properties will never achieve its ontological account
of objects. At every mereological level, unity will require objects at a lower
level, and so on.

But if this is a problem for the bundle theorist, it seems
to be merely a problem of analysis or description. At every
mereological level, one's account of unity will always involve, via (CU),
the concept of an object, and in this sense objects will never be "expunged."
But I'm concerned, not with a reductive analysis or description of objecthood,
but with giving an ontological picture in which the world of objects is a world
of unified properties. And (CU) combines with a bundle theory to paint such
a picture.[31]

In any case,
I don't think that the bundle theorist has to confront Armstrong's objection,
for I doubt that objects could be complex all the way down. There must be simple
objects if there are objects at all. My reason for thinking this is a familiar
one: Complex objects depend on their parts for their existence. Ontologically,
a complex object "passes the buck," so to speak, to its parts--this is in fact
a corollary of (P). Now if objects are complex all the way down, then this
ontological buck will continue to be passed. But then it seems evident that
there would be no objects at all. If the buck doesn't stop anywhere, if no
objects exist in their own rights, then none will exist at all.[32]

2. Substantial
and Qualitative Simplicity Coincide

If there are substantially simple objects,
however, then a different principle of unity will be needed for them, since
simples do not have structural properties.[33]
Even if we allow simples to have structural properties in a trivial sense,
(CU) cannot serve as an informative principle of qualitative unity for simples.
Suppose, that is, we let the properties of a substantial simple S be "structured
on" the 'parts' of S, namely on S itself, which is, after
all, a (non-proper) part of S. Still, for these properties
to be structured on S is for them to be properties of
S, and so we are back
where we started. (CU) is useless for substantial simples.

At this point the
bundle theorist would seem to have no choice but to appeal to a brute, perhaps
modal, relation among properties as the principle of qualitative unity for
simples. No Mysteries, however, counsels us to keep looking before
resorting to such a measure. To this end, I want to explore one fairly radical
proposal, and that's that the principle of qualitative unity for a simple object
is identity.
A simple object, that is, just is a single, simple property.[34]
This would provide an elegant account of unity for simple objects. The bundle
theorist would not have to worry about how distinct simple properties become
unified, for distinct simple properties are never unified into a (simple)
object. The proposed principle of qualitative unity for substantial simples
then looks like this:

(SU) For
any substantially simple object O and properties F and G: F and G are qualitative
parts of O iff F and G are each identical with O.

It's a corollary of (SU),
of course, that the F and G in question are identical with
each other.

Unlike
the defense of (CU), the defense of (SU) cannot appeal to ordinary examples,
for simples are not ordinary objects. My defense of (SU), rather, will consist
in answering some objections.

Objection I: It's just a category mistake to
say that a simple object is a property. Objects and properties belong to
different ontological categories, so that saying an object is a property
is like saying an event is a proposition, or that the number two is alive.

In reply, I should
first say that if I'm making a category mistake here, it's one that bundle
theorists have been making all along. If there are conjunctive properties,
so that any two unified properties F and G result in the
property F&G,
then even a substantially complex object will be a property.[35]
Alpha, for example, will be the conjunctive property this yellowness & this
roundness & this
fuzziness, etc. But while the bundle theory may have its faults, I don't
think that here, at the very outset, it's committing something as egregious
as a category mistake. And if it's not a category mistake to say that a macroscopic
object is a (conjunctive) property, then I don't see why it's a category mistake
to say that a simple object is a property.

That said, perhaps it will require
some conceptual revision to think of a simple object as a property. But I think
we should expect that our everyday distinctions will not apply straightforwardly
to the world of simples, which is far removed from common-sense. Campbell writes
of "[t]he way concrete particularity dissolves in the subatomic world",[36]
suggesting that we have good empirical reasons (from modern physics) to think
that our commonsense conceptions of properties and objects will not straightforwardly
apply to the very small

Objection II: A simple object cannot be a single property
because such a property would be "free-floating". But properties are dependent entities.
It's impossible for a property to exist without being the property of some
object.

Well, first of all, the "free-floating" properties I'm postulating
are objects (namely, simple objects), and so cannot exist independently
of objects. Nevertheless, it's true that the simples (SU) describes are free-floating
in the sense that they are not properties of objects, nor are they
unified with any other properties. But why can't there be free-floating
properties in this sense? Perhaps the intuition against such properties comes
from focusing only on examples from the macroscopic world. As I mentioned in
the last section, I grant that Alpha's properties (e.g., its color) could not
exist without being unified with other properties--indeed, not only do I grant
this, (CU) explains it. But it doesn't follow from this that simple
properties can't exist in isolation, for (CU) does not subsume such properties.

It will be clear by now, then, that
I reject the features used earlier to distinguish qualitative parts from substantial
parts; at least, I reject these features when they are said to apply to simples,
for a simple qualitative part just is a simple substantial part. Simple properties,
unlike complex properties, can be independent, arranged, and additive. It is
in this respect that I cannot accept (1)-(3) without qualification.

Objection
III: Suppose it turns out that (SU) is right, so that at the most fundamental
level, an object is a property. One might just as easily say in that case
that at the fundamental level, it turns out that a property is an object.
We thus lose the bundle theorist's claim that the world of objects is a world
of unified properties. If the object-property distinction dissolves at the
lowest level, then so does the bundle theory.

According to the objector, if the bundle theorist
asserts that, at most basic level,

(i) An object is a property,

then this is
equivalent to asserting that

(ii) A property is an object.

Since (ii) gives
doesn't give ontological priority to properties, neither does (i), so we've
lost a handle on the sense in which this is a property bundle theory,
at least at this fundamental level.

That there's something wrong with this reasoning
can be seen by considering two ways one might describe Spinoza's theological
views:

(i*) God is the physical universe.

(ii*) The physical universe is God.

There are contexts in which these express
(or pragmatically imply: this distinction is not important here) different
propositions. One might use (i*) to demote God to the status of the
physical universe. God, according to (i*), isn't as interesting as we thought:
he's not a mind, he's not omnipotent, etc. By contrast, one might use (ii*)
to promote the physical universe to the status of God. The universe
is more interesting than we thought: it is a mind, it is omnipotent, etc.

(i) and (ii) work the
same way. By asserting (i), I am not asserting (ii). In (i), 'property' takes
priority, so that the features traditionally associated with properties--being
a nature, a way of being--are ascribed to objects. Simple objects, according
to (i), are stranger than we thought: they are themselves ways of being. Contrast
this with (ii), which demotes properties in way unacceptable to the
bundle theorist. (ii) is something that might be asserted by a "blob" theorist,
someone who reduces properties to (or eliminates them in favor of) nature-less
objects. The objector is right that (ii) loses the sense in which properties
have ontological priority. For this reason I reject (ii) but accept (i).[37]

Notes

[1] I use 'substratum' and its
plural to refer to those things, not themselves ways of being, that are alleged
to underlie and support properties. The term is thus meant to cover traditional
Lockean substrata as well as the "refurbished"
substrata defended in Martin (1980) and the Aristotelian substances defended
in, e.g., Loux (1978). I will here use 'substance' and 'object' as terms neutral
between the bundle theory and these rivals.

[2] They are distinguished in Bennett
(1987, p. 212) and McCann (2001).

[4] I will not,
then, address the important objection of Van Cleve (1985), Hoffman and Rosenkrantz
(1996, §1.4), and others that the bundle theory is incompatible with objects'
changing and their having some of their properties only accidentally. Such
an objection threatens at most the identity version of the bundle theory, not
the supervenience or elimination versions. (Even the identity version can answer
the objection if allowed the resources of four-dimensionalism and counterpart
theory: see Hawthorne and Cover (1998).) In general, I will not discuss issues
of diachronic unity in this paper; synchronic unity will be difficult enough.

[5] Trope-theory
is on the rise, thanks in large part to the work of Keith Campbell (1981; 1990).
It is now one of the primary players in the theory of properties. See, e.g.,
Martin (1980), Bacon (1995), Ehring (1997), Lowe (1998), Maurin (2002), and
Heil (2003). Even David Armstrong, long a proponent of universals, believes
that tropes are on (almost) equal footing with his own favored view: see, e.g.,
Armstrong (1997, 3.23). Alas, enthusiasm about tropes is not universal. Recent
critics include Moreland (1985), Hochberg (1988), and Daly (1997).

[6] Hoffman
and Rosenkrantz (1997, p. 30); see also Martin (1980) and Thompson (1983, p.
201). Even Denkel (1992) and Simons (1994), in the course of defending the
bundle theory, deny that properties are parts of objects.

[8] They would include van Inwagen (1994), who would, I assume, also
object to the alternatives I present next. He cannot understand these terms
because they cannot be translated into what he takes to be a more perspicuous
mereological idiom.

[9] Here one must take the table
to be what Armstrong (1989a; 1997) calls a 'thick particular'.

[10] A principle of unity will
explain what some bundle theorists call the 'compresence' or 'concurrence'
of properties, terms I'll avoid because of the connotations they've acquired
in the literature. I'll sometimes use 'principle of unity' for a relation among
parts, other times for the linguistic formulation capturing this relation.
No confusion should result

[17] See Armstrong
(1978b, pp. 68-71). A structural property appears to be quite similar to what
Kim (1998, p. 84) calls a micro-based property, though as the examples
to follow show, there's nothing in the definition of a structural property,
as I conceive of it, requiring the relevant parts to be microscopic. I will
use the language of composition to describe the relation between a structural
property and the relevant "smaller" properties and relations, though some may
prefer to use the language of identity or supervenience. There are some philosophers
who would object to properties' being composed of others. Maurin (2002, p.
71) is apparently one of them; cf. also Lowe (1995, pp. 512-3).

[18] The example
is from Lewis (1986). Lewis' arguments in this paper are against structural
universals and do not threaten the structural properties I'm discussing here,
which are not universals but tropes--cf. Campbell (1990, §2.7).

[24] (CU*) would certainly be
needed to accommodate emergent properties, which, if there are such,
are even more robustly autonomous than the higher-level properties discussed
so far; see, e.g., O'Connor (1994) and Kim (1999). I cannot discuss emergent
properties here, except to say that what independent reasons there are for
favoring the bundle theory in general, and (CU) in particular, can be used
to build a case against such properties.

[25] For a collection of papers on this problem, see Rea
(1997), and for a discussion of the problem in the context of the bundle theory,
Paul (2002).

[26] Here and below, 'modal
properties' should be taken to mean alleged modal
properties.

[31] Hawthorne and Cover (1998, p. 215) appear to offer a similar
reply to Armstrong.

[32] For a recent version of this argument, see Lowe (1998,
pp. 158, 171).

[33] Simples, then, don't even
have spatial parts, since I take it anything with spatial parts has structural
properties.

[34] Armstrong (1989a, pp.
115-16) reports that David Lewis suggested a view like this to him. Cf. also
Kris McDaniel's "Brutal Simples" (unpublished manuscript), in which he considers
(and rejects) the view that a simple is a (natural) property.

[35] Cf. Armstrong's
(1989a; 1997) view that a (thick) particular is a state of affairs.

[37] An early draft of this paper was completed
while I was the recipient of a Summer Stipend from the National Endowment for
the Humanities. Much of the subsequent work was completed while I was on sabbatical
from Davidson College and a visiting scholar at the University of Colorado
at Boulder. I thank all three institutions for their support. Thanks also to
John Heil, David Barnett, Jonathan Lowe, Dan Korman, Matthew Stuart, Bob Pasnau,
and especially an anonymous referee for helpful discussion of these issues
and/or written comments on drafts.